Delhi's RRTS Station will clear Hazrat Nizamuddin congestion

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A dedicated pick-up and drop-off zone with the capacity to accommodate 40 vehicles and parking for 15 buses simultaneously is being planned at the Sarai Kale Khan RRTS station, according to officials close to the project. The entire section will be set up under the RRTS station's elevated structure, which will function as a city bus interchange point. Additionally, commuters will have segregated pathways, allowing passengers to enter the station without encountering any motor vehicles.


This project is part of the multi-modal integration plan for the Namo Bharat train at Sarai Kale Khan and Anand Vihar stations. The Sarai Kale Khan station is strategically located near the busy Hazrat Nizamuddin Railway Station, Delhi's Pink Line station, Veer Haqeeqat Rai ISBT, a city bus depot, and the Ring Road. All these transport hubs are planned to be interconnected at the RRTS station, as reported by the Hindustan Times, quoting officials from the National Capital Region Transport Corporation (NCRTC).
An NCRTC spokesperson mentioned that, given its prime location, this new major transport hub is expected to serve a large number of passengers. To facilitate easier travel and ensure smooth movement around the RRTS station, NCRTC is creating a user-friendly environment with dedicated pick-up and drop-off areas, pedestrian pathways, a footbridge (FOB), and travelators.
With this infrastructure, commuters will no longer need to cross roads or deal with traffic when changing transport modes. Currently, many intercity buses pick up and drop off passengers along the roadside at the Sarai Kale Khan bus stop. The spokesperson added that due to the lack of designated space, commercial and private vehicles often drop off passengers on the road, leading to traffic disruptions and unsafe conditions for passengers, who are forced to cross the crowded and congested road.
The Sarai Kale Khan station is being planned to connect with other transport options, including the bus stand, railway station, and Metro station. As part of this plan, the NCRTC has also decided to create five entry and exit gates with multiple staircases, lifts, and escalators.
As the largest RRTS station, Sarai Kale Khan will measure 215 metres in length, 50 metres in width, and 15 metres in height, and will feature 14 lifts and 18 escalators. A footbridge with six travelators is being constructed to link the RRTS station with the railway station, which is 280 metres away. The Sarai Kale Khan station is part of the 82-kilometre Delhi-Ghaziabad-Meerut RRTS corridor and will also serve as an interchange for two additional planned RRTS lines.


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World Bank to help develop Haryana RRTS projects including Delhi-Gurugram line

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World Bank and NCRTC discussed financing and developing RRTS projects in Haryana, focusing on the Delhi-Gurugram line. The collaboration aims for sustainable transport.

A delegation from the World Bank met on Friday met officials of the National Capital Region Transport Corporation (NCRTC) in the Capital to discuss the modalities of financing and developing Regional Rapid Transit System (RRTS) projects in Haryana, particularly the Delhi to Gurugram line.

NCRTC — the agency executing the RRTS project — is already developing one RRTS line — Delhi to Meerut, which is partially operational at present. Last year, the Haryana government had approved the Delhi-Gurugram RRTS project — which will later be extended to Alwar in Rajasthan — and the Delhi-Panipat RRTS project.

An NCRTC spokesperson said that a delegation led by World Bank regional director for infrastructure Pankaj Gupta met an NCRTC team led by its managing director Shalabh Gupta at its corporate office in Delhi.

“The bank, apart from funding the projects, is handholding the RRTS projects and is partnering on various initiatives such as development of logistics services, capturing land value through RRTS corridors and exploring transit-oriented development along these corridors. The objective is to develop sustainable and efficient transport infrastructure in NCR,” the spokesperson said.

Puneet Vats, chief public relations officer, NCRTC said that the collaboration with World Bank will not only focus on getting financial support, but both sides will also work on sharing advanced knowledge and technologies. “The World Bank has global expertise and we want to take advantage of that. The World Bank team also appreciated the technical expertise and new technologies that have been deployed on the Delhi-Meerut corridor,” he said.

NCRTC plans to construct the Delhi-Alwar RRTS corridor in three phases. In the first phase, the agency will construct a 107-km stretch from Sarai Kale Khan in Delhi to Shahjahanpur-Neemrana-Behror (SNB) urban complex, passing through Gurugram, Manesar, Panchgaon and Rewari. In the second phase, the line will be extended from SNB to Sotanala, an industrial town in Rajasthan, and in the third phase, the corridor will extend as far as Alwar.

Vats said NCRTC has completed pre-construction activities along the proposed alignment for the first phase. “We have also identified land that will be required for constructing the stations and depots, and discussion is on to get it transferred to NCRTC... As soon as the project gets approval from the central government, work on it will start,” he said.

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Linear Regression | Hypothesis Testing

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Help from ChatGPT



I saw this screen in a video for t-test for slope. Can you shed some light as to what is being taught here?

Answer

The screen you are seeing explains how to perform a t-test for the slope of a simple linear regression model. The goal is to assess whether the slope ($b_1$) of the regression line is statistically significantly different from zero, which would indicate a linear relationship between the dependent and independent variables.
Here's an explanation of the components shown in the image:
t-Statistic for the Slope:
Formula: $t = \frac{b_1}{SE(b_1)}$
$b_1$ is the estimated slope of the regression line.
$SE(b_1)$ is the standard error of the slope estimate, which measures the variability of the slope coefficient across different samples.
This formula is used to calculate the t-statistic for the slope. The t-statistic quantifies how many standard errors the estimated slope is away from zero.
Standard Error of the Slope $SE(b_1)$:
The standard error $SE(b_1)$ of the slope is calculated using the formula:
$$SE(b_1) = \sqrt{\frac{\sum (y_i - \hat{y}_i)^2}{n - 2}} \div \sqrt{\sum (x_i - \bar{x})^2}$$
Numerator:
$\sum (y_i - \hat{y}_i)^2$ is the sum of squared residuals (SSR), where $y_i$ are the actual values of the dependent variable and $\hat{y}_i$ are the predicted values from the regression model.
$n - 2$ accounts for the degrees of freedom. Since two parameters are estimated in a simple linear regression (the intercept and the slope), we subtract 2 from the total number of data points $n$.
Denominator:
$\sum (x_i - \bar{x})^2$ is the sum of squared deviations of the independent variable $x$ from its mean $\bar{x}$. This reflects how much variability exists in the independent variable $x$.
Interpretation:
t-Statistic: Once the t-statistic is calculated, you compare it to the critical value from the t-distribution (based on the degrees of freedom and the desired significance level, e.g., 0.05). If the t-statistic is greater in magnitude than the critical value, you reject the null hypothesis that the slope is zero.
Null Hypothesis ($H_0$): $b_1 = 0$. This means that there is no linear relationship between the variables.
Alternative Hypothesis ($H_1$): $b_1 \neq 0$. This suggests a linear relationship between the variables.
If the null hypothesis is rejected, it implies that there is a statistically significant linear relationship between the independent and dependent variables.
In summary, this screen is demonstrating how to perform a t-test on the slope of a regression line to check whether the slope is significantly different from zero, indicating a linear relationship between the two variables. The t-test is based on the ratio of the slope to its standard error, and the standard error itself is calculated using the residuals from the regression and the variability of the independent variable.

Tags: Machine Learning,Mathematical Foundations for Data Science,

Summary of Support Vector Machines (SVM) - Based on Video by Intuitive Machine Learning

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Support Vector Machines (SVM) are among the top non-linear supervised learning models.

SVMs help identify the optimal hyperplane to categorize data. In one dimension, a hyperplane is a point; in two dimensions, it’s a line; and in three dimensions, it’s a surface that separates positive and negative categories.

Linear Model: For linearly separable data, there are multiple ways to draw a hyperplane that separates positive and negative samples. 



While all hyperplanes separate the categories, SVMs help choose the best one by maximizing the margin, earning them the name “maximum margin classifier.”

What is a support vector? Support vectors are the data points closest to the hyperplane. 



Identifying these crucial data points, whether negative or positive, is a key challenge that SVMs address.

Unlike other models like linear regression or neural networks, where all data points influence the final optimization, in SVMs, only support vectors impact the final decision boundary. When a support vector moves, the decision boundary changes, but moving other vectors has no effect.

Similar to other machine learning models: 



SVMs optimize weights so that only support vectors determine the weights and the decision boundary.

Understanding the mathematical process behind SVMs requires knowledge of linear algebra and optimization theory. Before diving into model calculations, it’s important to understand H0, H1, H2, and W, as shown in the image. W is drawn perpendicular to H0. 



Equation for ( H_0 )



The equation for the hyperplane ( H_0 ) is ( W dot X + b = 0 ). This applies to any number of dimensions. For example, in a two-dimensional scenario, the equation becomes ( W_1 dot X_1 + W_2 dot X_2 + b = y ).

Since ( H_0 ) is defined as ( W dot X + b = 0 ):

( H_1 ) is ( W dot X + b \geq 0 ), which can be rewritten as ( W dot X + b = k ), where ( k ) is a variable. For easier mathematical calculations, we set ( k = 1 ), so ( W dot X + b = 1 ).
( H_2 ) is ( W dot X + b < 0 ), which can be rewritten as ( W dot X + b = -k ). Again, setting ( k = 1 ), we get ( W dot X + b = -1 ).

Applying Lagrange Multipliers

Lagrange Multipliers help identify local maxima and minima subject to equality constraints, forming the decision rule. The assumption here is that the data is linearly separable with no outliers, known as Hard Margin SVM. 



Handling Noise and Outliers

If the data contains noise or outliers, Hard Margin SVM fails to optimize. To address this, Soft Margin SVM is used.

By adding “theta” as constraints to the optimization problem, it becomes possible to satisfy constraints even if outliers do not meet the original constraints. However, this requires a large volume of data where all examples satisfy the constraints.

Regularization:

One technique to handle this problem is Regularization. L1 regularization can be used to penalize large values of theta, with a constant “C” as the regularization parameter. If ( C ) is small, theta is significant; otherwise, it is less important.

Setting ( C ) to a positive infinite value results in the same output as Hard Margin SVM.
A smaller ( C ) value results in a wider margin, while a larger ( C ) value results in a narrower margin. A narrow margin is less tolerant to outliers.
This way, Soft Margin SVM can handle non-linearly separable data with outliers and noise.

Kernel Trick

When data is inherently non-linearly separable, as shown in the example below, the solution is to use the kernel trick. 



The kernel trick introduces a variable ( k ) that squares ( x ), helping to solve the problem. This approach is derived from applying the Lagrange equation. By squaring ( x ), we can achieve a clear separation of the data, allowing us to draw a separating line. 



Polynomial Kernel

This kernel uses two parameters: a constant ( C ) and the degree of freedom ( d ). A larger ( d ) value makes the boundary more complex, which might result in overfitting. 



RBF Kernel (Gaussian Kernel)

The RBF kernel has one parameter, ( gamma ). A smaller ( gamma ) value leads to a linear SVM, while a larger value heavily impacts the support vectors and may result in overfitting.

Tags: Machine Learning,Mathematical Foundations for Data Science,Mariswaran

160 kmph speed, 135 km corridor, know all about Orbital rail which will change face of Delhi-NCR, project is worth Rs...

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Spanning 135 kilometres, this high-speed rail corridor promises to ease the overburdened roads and railway lines of Delhi-NCR. The project is expected to link key logistics hubs in Haryana and Uttar Pradesh

Updated : Aug 24, 2024, 06:29 AM IST

160 kmph speed, 135 km corridor, know all about Orbital rail which will change face of Delhi-NCR, project is worth Rs...

Eastern Orbital Rail Corridor project

The relentless traffic congestion of Delhi-NCR could soon become a thing of the past. But the solution isn’t on the roads—it’s racing along tracks at a staggering speed of 160 km per hour. The Eastern Orbital Rail Corridor, a bold new project, is set to revolutionise the way we think about regional transport. But what exactly is this ambitious undertaking, and how will it change the daily grind of millions?

The Ghaziabad Development Authority (GDA) has been entrusted with a monumental task: spearheading the Eastern Orbital Rail Corridor project as the nodal agency. The government’s decision to hand over the responsibility to GDA includes the critical task of preparing a comprehensive feasibility report. To ensure a thorough evaluation, the GDA will gather funds from stakeholders who stand to benefit from this groundbreaking initiative. The report will then be forwarded to the Haryana Rail Infrastructure Development Corporation (HRIDC) for final assessment.

Spanning 135 kilometres, this high-speed rail corridor promises to ease the overburdened roads and railway lines of Delhi-NCR. The project is expected to link key logistics hubs in Haryana and Uttar Pradesh, integrating seamlessly with national highways, railway lines, and even the upcoming Jewar International Airport. This interconnectedness is anticipated to spur significant industrial growth in the region.

TRENDING NOW

The corridor’s construction will demand an estimated investment of ₹14,000 crore, with ₹11,000 crore earmarked for infrastructure and ₹3,000 crore for land acquisition. The corridor will feature 18 strategically placed stations, 12 of which will serve as crossing points, while six will function as halt stations. The passenger trains are designed to zip along at 160 km per hour, while freight trains will travel at 100 km per hour, ensuring swift and efficient movement of both people and goods.

Covering 90 kilometres in Uttar Pradesh and 45 kilometres in Haryana, this corridor will provide substantial benefits to areas such as Jewar Airport, Dadri, Greater Noida, Ghaziabad, and Meerut. Its strategic alignment will intersect with multiple railway lines, rivers, and highways, promising to reduce pollution, ease traffic, and boost regional connectivity.
With the Eastern Orbital Rail Corridor set to redefine transportation in NCR, the future of commuting in this bustling region has never looked more promising.

[ Ref ]

What is Machine Learning? (Learn From Instructors From Google)

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Machine learning:

A program or system that trains a model from input data. The trained model can make useful predictions from new (never-before-seen) data drawn from the same distribution as the one used to train the model.

Machine learning also refers to the field of study concerned with these programs or systems.

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What is Machine Learning as per Tom Mitchell?

Tom Mitchell, one of the pioneers of machine learning, provided a widely accepted formal definition of machine learning in his book "Machine Learning" (1997):
"A computer program is said to learn from experience $E$ with respect to some class of tasks $T$ and performance measure $P$, if its performance at tasks in $T$, as measured by $P$, improves with experience $E$."
Explanation of the Definition:
Task $T$: This is the specific task that the program is designed to perform. For example, predicting house prices, recognizing images of animals, or classifying emails as spam or not spam.
Experience $E$: This refers to the data or experience the program is exposed to. For instance, this could be past house price data, labeled images of animals, or emails previously classified as spam or not spam.
Performance Measure $P$: This is a way to measure how well the program is doing at the task. For example, it could be the accuracy of predictions, error rates, or any other metric appropriate for the task.
In essence, machine learning is about creating programs that improve their performance at certain tasks based on data (experience), without being explicitly programmed to perform those tasks.


What are your thoughts on this definition:
Traditional programming is getting output from input data and rules. Machine Learning is getting the rules back for input and resultant data.

Your definition is a succinct and intuitive way to distinguish traditional programming from machine learning. Here's a deeper analysis:
Traditional Programming:
Definition: Traditional programming involves writing explicit rules or instructions for the computer to follow in order to process input data and produce the desired output.
Process: You provide:
Input data
Rules (defined by the programmer)
Output (computed by applying the rules to the input)
Machine Learning:
Definition: In machine learning, instead of explicitly coding the rules, the model learns these rules or patterns from the data. The goal is to find an underlying function or model that best maps the input data to the output (results).
Process: You provide:
Input data
Output data (results)
The machine learning algorithm finds or "learns" the rules (or model) that map the input to the output.
Key Differences:
Rules vs. Learning:
In traditional programming, rules are manually coded based on the programmer's understanding.
In machine learning, the model autonomously learns the rules or patterns from the data through training.
Example:
Traditional Programming: If you want to classify an email as spam, you'd write explicit rules like "If the email contains the word 'free' more than twice, classify it as spam."
Machine Learning: You'd provide a machine learning model with a large set of labeled emails (some marked as spam, some not), and the model would automatically figure out what features (words, patterns) are indicative of spam without explicitly coding the rules.
Summary:
Your definition captures the essence of machine learning well: instead of manually defining the rules (as in traditional programming), machine learning infers these rules from data. It's a shift from deterministic rule-based systems to data-driven pattern recognition, enabling more complex, adaptive solutions.

Tags: Machine Learning,Technology,